Automata and Computability - Show that the problem of testing whether two branching programs compute the same function is solvable in polynomial time if and only if P = NP

Algorithm Problem - Argue briefly that to test whether a given n-element permutation can be sorted by an n-input comparison network, it suffices to test the network on n—1 sequences of 0’s and 1’s.

Algorithm Problem - The sum of n k-bit numbers can be computed by a combinational arithmetic circuit as follows. Assume n is an exact power of 2. the circuit consists of a complete binary tree of ripple-carry adders, in which each node in the tree adds two numbers and produces a sum which is fed to its parent. The n/2 leaves of the tree input the n k-bit numbers, and the total sum is produced a...

Algorithm Problem - a. Consider an n-element list in an n-processor EREW parallel random-access machine, where some elements of the list are marked as being blue. Describe an efficient parallel algorithm to form a new list consisting of all the blue elements. Analyze your algorithm. b. Suppose that some nodes in an n-node binary tree are marked blue. Describe an efficient EREW algorithm to f...

Algorithm Problem - Mr. Johnson draws an n-input comparison network with m comparators according to the following conventions. The lines of the network go left-to-right, and comparators are drawn vertically to connect two lines. The network is drawn on an underlying grid, so that each comparator occupies one of at most m columns. Comparators can share columns, but they do not overlap. An examp...